A DFT analysis of the effect of chelate ring size on metal ion selectivity in complexes of polyamine ligands

Polyhedron xxx (2012) xxx–xxx

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A DFT analysis of the effect of chelate ring size on metal ion selectivity in complexes of polyamine ligands Robert D. Hancock a,⇑, Libero J. Bartolotti b a b

Department of Chemistry and Biochemistry, University of North Carolina at Wilmington, Wilmington, NC 28403, USA Department of Chemistry, East Carolina University, Greenville, NC 27858, USA

a r t i c l e

i n f o

Article history: Available online xxxx This paper is dedicated to Alfred Werner in the Centenary year of his award of the Nobel Prize for his development of theories that are fundamental to modern inorganic chemistry. Keywords: DFT calculations Formation constants Polyamine ligands Ligand selectivity Ligand design Chelate ring size effects

a b s t r a c t DFT calculations were carried out using the DMOL3 program to investigate the thermodynamics of complex formation of polyamine complexes of M(II) ions (M = metal) in the gas-phase, and in aqueous solution, where the COSMO module of DMOL3 models aqueous solution as a structureless dielectric medium with a dielectric constant appropriate for water. The calculations that included relativistic effects employed the all electron scalar relativity option available in DMOL3. The values of DH(aq)(DFT) and DG(aq)(DFT) for reactions such as [M(H2O)6]2+ + en = [M(H2O)4en]2+ + 2H2O (en = ethylenediamine) in aqueous solution for M = Ca, Cr, Mn, Fe, Co, Ni, Cu, Zn, and Cd were found to correlate well with the corresponding values in aqueous solution. Values of DH(g)(DFT) for reactions such as [M(H2O)4en]2+ + tn = [M(H2O)4tn]2+ + en (tn = 1,3-diaminopropane) calculated in the gas-phase for M = Ca, Cr, . . . Cu showed the effect of changing chelate ring size from 5-membered for en to 6-membered for tn in that complexes of smaller metal ions such as Cu(II) were less destabilized by the increase in chelate ring size than larger metal ions such as Ca(II). This supports the chelate ring-size rule (R.D. Hancock, A.E. Martell, Chem. Rev. 89 (1989) 1875) that states that increase of chelate ring size stabilizes the complexes of smaller metal ions relative to those of larger metal ions. Use of COSMO to simulate the change from the en to the tn complexes in aqueous solution showed only a small response to change in metal ion size, as is found to be the case experimentally. An important aspect here is that the change in log K1 on changing chelate ring size in passing en to tn complexes is of the same order of magnitude as the probable uncertainty in the energies obtained from the DFT calculations. The DFT calculations show how aqueous solution dampens out chelate effects for small ligands such as en and tn, and also removes the effects of polarizability seen in the gas-phase. The chelate ring size rule is supported by calculations on Ni(II) complexes of pairs of polyamine ligands such as dien (diethylenetriamine) and dptn (1,5,9-triazanonane), or trien (triethylenetetramine) and 2,3,2-tet (1,4,8,11-tetraazaundecane), where the first member of the pair of ligands forms only 5-membered chelate rings, while the second member forms at least one 6-membered chelate ring in place of a 5membered chelate ring formed by the first member. The DFT calculations show that increase of chelate ring size usually leads to a decrease in stability of the Ni(II) complex, but correctly predict that the 2,3,2tet complex will be more stable than the trien complex, which is an unusual example where replacing a 5-membered chelate ring with a 6-membered chelate ring leads to higher complex stability. The role of polarizability effects in the thermodynamics of complex-formation is discussed. Polarizability effects stabilize complexes of larger ligands such as dptn relative to those of smaller analogs such as dien in the gasphase by more effectively dispersing the cationic charge over the complex. Also discussed is the possible role of specific solvation by water molecules in the thermodynamics of complex-formation in aqueous solution, which effect is not taken into account by the COSMO module used in this paper. Ó 2012 Elsevier Ltd. All rights reserved.

1. Introduction Control of metal ion selectivity [1] is important in a variety of areas, ranging from design of ligands for removal of possibly disease-causing metal ions such as Cu(II) and Zn(II) in Alzheimer’s ⇑ Corresponding author. Tel.: +1 910 962 3025; fax: +1 910 962 3013. E-mail address: [email protected] (R.D. Hancock).

disease [2,3] and Fe(III) in Parkinson’s disease [4], to selective removal of Am(III) and Cm(III) from mixtures of Ln(III) ions in the treatment of nuclear waste [5,6]. A primary factor considered in ligand design [1] is the choice of donor atoms, which is largely based on the HSAB principle of Pearson [7,8], and expected geometrical preferences of the metal ion. Thereafter architectural features of the ligand are considered, particularly the level of preorganization [9]. A more preorganized ligand is, as the free ligand, more nearly

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restricted to the conformation required for complexing the target metal ion. Familiar examples of preorganized ligands are the crown-ethers [10], cryptands [11], and N-donor macrocycles [12]. Non-cyclic ligands such as PDA [13–15], DPP [16], DPA [17], PDALC [18], or PDAM [19] (see Fig. 1 for key to ligand abbreviations) are examples of highly preorganized ligands based on the rigid phen backbone, where the preorganization derives from a rigid cleft rather than a macrocyclic structure. A less-obvious example of what can be regarded as preorganization is that of chelate ring size [1,20]. A large amount of experimental evidence [1,20] supports the idea that 5-membered chelate rings form complexes of the lowest steric strain with larger metal ions with an ionic radius in the vicinity of 1.0 Å, while 6-membered chelate rings form with the lowest strain with very small metal ions such as Be(II), with ionic radii in the vicinity of 0.3 Å. This is summarized in the following graphic: The analysis of the best-fit geometry for coordinating as part of 5-membered en and 6-membered tn chelate rings was previously carried out with MM (molecular mechanics) calculations [21–26]. DFT (Density Functional Theory) has proved to be a powerful tool [27] in predicting many properties of inorganic compounds, including molecular structures, and a variety of spectra, including vibrational, absorption, circular dichroism, magnetic circular dichroism, resonance Raman, X-ray absorption, Mössbauer and EPR spectra. DFT has been used [28–32] to calculate gas-phase free energies of reactions that can be correlated with the corresponding reactions in aqueous solution to predict experimentally unknown log K1 (or DG(aq) = RT ln K) values. Thus, log K1 values for the NH3 complexes of a wide variety of metal ions were correlated with the DG(g)(DFT) values in the gas phase for reaction (1):

½MðH2 OÞ6 nþ ðgÞ þ NH3 ðgÞ ! ½MðH2 OÞ5 NH3 nþ ðgÞ þ H2 OðgÞ

ð1Þ

Note: Log K1 values refer here to the equilibrium constant K = [ML]/ [M][L], where ML is the complex formed from the metal ion M and

O

N

N

N

O-

-

O

O

OH

PDA

H2N

N

N

H H2N

trien (2,2,2-tet) H2N

2,3,2-tet

NH2

H2N

tn

en

H

H N NH2

NH2

dien

NH2

N

R

N

HN N NH N N R N R H

L1(R = aromatic group)

NH2

H2N

dptn

The result of this particular correlation for M(II) ions is seen in Fig. 3. The coefficient of determination (R2) for the correlation is good at 0.975. The point for Ru(II) on the correlation is not experimental, but shows how the calculated DG(g)(DFT) value for the Ru(II)/en complex can be used to estimate log K1(en) = 10.1 for Ru(II). Where MM has proved particularly powerful is in its ability to isolate steric from electronic effects. Thus, MM was used [21] to rationalize the difference in DH for reactions where a ligand with only 5-membered chelate rings was displaced from the complex by one with one or more of the 5-membered chelate rings replaced by 6-membered chelate rings. The difference in log K for the formation of complexes where 5-membered chelate rings are present, and those where 6-membered chelate rings are present, is due almost entirely to differences in DH, with little difference in DS [20]. This supports the idea that the generally lower log K values for complexes of ligands that form 6-membered chelate rings than for analogs with 5-membered chelate rings are due to greater steric strain. The results of the MM calculations are summarized in Table 1. Particularly interesting is the case for the pair of ligands trien and 2,3,2-tet, where the presence of a 6-membered chelate ring in the 2,3,2-tet Ni(II) complex actually raises the stability, which effect is reproduced by the MM calculations.

8QP

N

NH2 H2N

ð2Þ

N

H N

½MðH2 OÞ6 nþ ðgÞ þ enðgÞ ! ½MðH2 OÞ4 ðenÞnþ ðgÞ þ 2H2 OðgÞ

DPP

N

H

N

NH2

N

N

DPA

PDAM

N

N

N

NH2

O

H N

HO

PDALC

N

O

N

N

ligand L, and, where available, are preferably those reported at an ionic strength of 0.1 in the critical compilation of Smith and Martell [33]. Experimental DG and DH values for complex-formation equilibria in aqueous solution are referred to as DG(aq) or DH(aq), while values calculated in the gas-phase by DFT are referred to as DG(g)(DFT) or DH(g)(DFT), and calculated by DFT in simulated aqueous solution are referred to as DG(aq)(DFT) or DH(aq)(DFT). An example of the use of Eq. (1) for NH3 complexes is seen in Fig. 2, where the calculated value of DG(g)(DFT), reported in this paper, for the Ru(II)/NH3 complex is used to predict that log K1 (NH3) for Ru(II) is 4.0. A similar approach is taken here with bidentate N-donor ligands such as en (ethylenediamine) and tn (1,3-diaminopropane). The DG(g)(DFT) values for reaction (2) are calculated, and correlated with experimental [33] log K1(NH3) values.

H N NH2 H2N

2,3-tri

Fig. 1. Ligands discussed in this paper.

Fig. 2. Correlation between DG(g)(DFT) for formation of the mono-NH3 complexes from the hexa-aquo ions for M(II) ions in the gas-phase and log K1(NH3) values in aqueous solution [33]. The equation for the least-squares best-fit line fitted to the experimental points is shown on the diagram, as well as R2, the coefficient of determination. The log K1(NH3) value for Ru(II), indicated in parentheses, is unknown, but the calculated value for DG(DFT) for the Ru(II)/NH3 complex reported here can be used to estimate that log K1(NH3) for Ru(II) is 4.0. The error bars on the points indicate the accuracy of about 1 kcal mol1 with which wave-mechanical calculations normally predict the energies of simple gas-phase reactions [51]. Note: 1 kcal = 4.184 kJ.

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Fig. 3. Correlation between DG(DFT) for formation of the mono-en complexes from the hexa-aquo ions for M(II) ions and log K1(en) values in aqueous solution [33]. The equation for the least-squares best-fit line fitted to the experimental points is shown on the diagram, as well as R2, the coefficient of determination. The log K1(en) value for Ru(II), indicated in parentheses, is unknown, but the calculated value for DG(DFT) for the Ru(II)/en complex can be used to estimate that log K1(en) for Ru(II) is 10.1. The DFT calculations were carried out in a structureless dielectric medium with a dielectric constant appropriate for water using the program COSMO.1 The equation for the least-squares best-fit line fitted to the experimental points is shown on the diagram, as well as R2, the coefficient of determination. The error bars on the points indicate the accuracy of about 1 kcal mol1 with which wavemechanical calculations normally predict the energies of simple gas-phase reactions [51]. Note: 1 kcal = 4.184 kJ.

Table 1 Changes in enthalpy in aqueous solution of complex formation of polyamine complexes of Ni(II) on increasing chelate ring size from five to six-membered, compareda with the differences in strain energy obtained from MM calculationb. Complexc

Ud

Ni(en) Ni(tn) Ni(en)2 Ni(tn)2 Ni(en)3 Ni(tn)3 Ni(dien) Ni(dptn) Ni(dien)2 Ni(dptn)2 Ni(trien) Ni(2,3,2-tet)

1.14 3.04 3.35 7.16 4.57 13.12 6.08 8.28 11.87 21.32 9.44 7.32

D U e 1.53 3.07 7.44 1.46 7.97 2.49

D Hf 9.3 7.9 18.1 15.3 28.0 21.6 11.9 10.6 26.3 17.6 14.0 17.9

D(DH) 1.4

shown in Tables 2–6. Ground state energies, Eel, optimized geometries and Hessians were calculated using the density functional [34] software package DMOL3 [35,36], both as gas-phase reactions, and in aqueous solution. The reactions in aqueous solution were simulated by carrying out the calculations using the COSMO module of DMOL3, which carries out the calculations in a structureless dielectric medium with a dielectric constant appropriate for water. The exchange–correlation energy was approximated by the Becke–Tsuneda–Hirao gradient-corrected functional [37,38]. Double numerical plus polarization basis sets, a 20 bohr cutoff and a fine integration grid were used in all calculations. The SCF convergence was set to 108 and convergence criteria for the gradient in geometry optimizations was set to 104 hartree per bohr. The calculations that included relativistic effects employed the all electron scalar relativity option available in DMOL3 [39]. The Hessian was calculated numerically using central differencing to obtain the second derivatives. Vibrational frequencies (mi) for each reactant and product were obtained from a normal mode analysis of the calculated Hessian matrix, from which translational and rotational degrees of freedom were projected [40]. The Eel, geometries and mi allowed the calculation of temperature dependent partition functions needed in the statistical mechanical expression for molecular free energies [41]. Table 2 Values of DE(g)(DFT), DE(g)(DFT)(zpe) (zero point energy corrected), DH(g)(DFT), and DG(g)(DFT) at 298 K (kcal mol1) for the reaction involving replacement of two H2O ligands by an en (ethylenediamine) ligand on the hexaaqua ion in the gas phase (Eq. (2)) for divalent metal ions, calculated in this work from DFT as described in the text. Ca2+

Sc2+

Ti2+

V2+

Cr2+

8.2176 10.5170 9.3739 19.0330

14.2471 15.8693 15.1048 22.1910

16.7126 17.7925 17.1715 23.8214

20.9258 21.8666 21.5128 28.0459

31.4596 32.3349 31.6965 40.1866

Mn2+

Fe2+

Co2+

Ni2+

Cu2+

DE(g)(DFT) DE(g)(DFT) (zpe) DH(g)(DFT) DG(g)(DFT)

19.2316 20.4302 19.8148 27.4907

23.3715 23.8925 23.5199 29.0570

28.2043 29.3799 28.7687 37.7183

30.0221 32.5624 31.0312 40.7935

40.9559 42.7600 41.5286 51.2119

Zn2+

Cd2+

Ru2+

DE(g)(DFT) DE(g)(DFT)(zpe) DH(g)(DFT) DG(g)(DFT)

26.5849 27.8327 27.1509 34.0592

25.0630 26.3841 25.6363 33.1158

40.5310 42.0204 41.0983 48.8450

DE(g)(DFT) DE(g)(DFT)(zpe) DH(g)(DFT) DG(g)(DFT)

2.8 2.8 1.3 7.7 3.9

a The difference in strain energy, DU, should be compared with the difference in enthalpy of complex formation, D(DH); units are kcal mol1. Note: 1 kcal = 4.184 kJ. b See Refs. [20–26]. c For key to ligand abbreviations, see Fig. 1. d This is the strain energy in kcal mol1 for the complex indicated. e This is the difference in strain energy of the complex forming only 5-membered chelate rings compared to the analogous complex with one or more 6-membered chelate rings, corrected for the differences in strain energy of the free ligands. f Ref. [33].

In view of the success of the approach where DFT has allowed for predictions of aqueous phase log K values for unidentate ligands such as NH3 [29–31] or OH [27,28], the interest here was to see how well DFT could predict log K values for complexes of polyamines, and in particular predict such subtle effects as that of chelate ring size on thermodynamic complex stability. 2. Experimental 2.1. Computational method The reaction free energies were obtained by performing electronic structure calculations on the reactants and the products

Table 3 Values of DE(g)(DFT), DE(g)(DFT)(zpe) (zero point energy corrected), DH(g)(DFT), and DG(g)(DFT) at 298 K (kcal mol1: Note: 1 kcal = 4.184 kJ) for the reaction involving replacement of two H2O ligands by a tn (1,3-diaminopropane) ligand on the hexaaqua ion in the gas phase (Eq. (2)) for divalent metal ions, calculated in this work from DFT as described in the text.

DE(g)(DFT) DE(g)(DFT)(zpe) DH(g)(DFT) DG(g)(DFT)

DE(g)(DFT) DE(g)(DFT)(zpe) DH(g)(DFT) DG(g)(DFT)

DE(g)(DFT) DE(g)(DFT)(zpe) DH(g)(DFT) DG

Ca2+

Sc2+

Ti2+

V2+

Cr2+

9.1220 10.9353 10.0749 18.2142

13.2877 14.1618 14.3360 21.6523

18.8475 20.2454 19.4650 26.3730

22.6242 23.3052 23.0662 28.8392

34.2671 34.6484 34.2432 41.6869

Mn2+

Fe2+

Co2+

Ni2+

Cu2+

21.1410 21.8702 21.4597 28.2908

25.5621 25.9669 25.6491 30.4722

28.4963 28.9072 28.6108 34.1598

32.4617 34.8356 33.3104 42.6497

45.2862 46.9595 45.7620 55.0242

Zn2+

Cd2+

Ru2+

29.0101 29.9422 29.3550 36.1232

27.2449 28.4002 27.7905 34.3821

43.0868 44.4821 43.5924 50.5724

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R.D. Hancock, L.J. Bartolotti / Polyhedron xxx (2012) xxx–xxx

Table 4 Values of DE, DE(zpe) (zero point energy corrected), DH, and DG at 298 K (kcal mol1) for the reaction involving replacement of two H2O ligands by an en (ethylenediamine) ligand on the hexaaqua ion in aqueous solution as simulated by the COSMO program (Eq. (2)) for divalent metal ions, calculated in this work from DFT as described in the text.

DE(aq)(DFT) DE(aq)(DFT)(zpe) DH(aq)(DFT) DG(aq)(DFT)

DE(aq)(DFT) DE(aq)(DFT)(zpe) DH(aq)(DFT) DG(aq)(DFT)

DE(aq)(DFT) DE(aq)(DFT)(zpe) DH(aq)(DFT) DG (aq)(DFT)

Ca2+

Sc2+

Ti2+

V2+

Cr2+

6.7218 8.4286 7.7264 16.1847

11.4813 12.8648 12.3817 18.9666

15.2630 15.4778 15.8223 18.9376

17.9610 20.0164 19.2259 27.5782

23.9402 25.0713 24.6287 31.9981

Mn2+

Fe2+

Co2+

Ni2+

Cu2+

16.4518 17.7908 17.3824 24.2745

18.6359 20.5680 19.7840 26.3885

21.9036 23.6052 22.9295 29.8972

24.4197 26.7204 25.7282 33.5177

33.7791 35.9851 34.9157 44.1724

Zn2+

Cd2+

Ru2+

21.8343 23.2639 22.6584 29.5577

20.9836 22.5203 21.9702 27.9558

35.2653 37.3645 36.5107 44.0123

Table 5 Values of DE, DE (zpe) (zero point energy corrected), DH, and DG at 298 K (kcal mol1: Note: 1 kcal = 4.184 kJ) for the reaction involving replacement of two H2O ligands by a tn (1,3-diaminopropane) ligand on the hexaaqua ion in aqueous solution as simulated by the COSMO program (Eq. (2)) for divalent metal ions, calculated in this work from DFT as described in the text. Ca2+

Sc2+

Ti2+

V2+

Cr2+

5.0803 6.4207 5.9580 13.1283

10.5891 11.3323 11.1898 16.1788

14.3190 14.9475 15.0589 18.7492

16.6868 18.4099 17.8091 24.8876

23.2037 24.4742 23.8659 31.3889

Mn2+

Fe2+

Co2+

Ni2+

Cu2+

DE(aq)(DFT) DE(aq)(DFT)(zpe) DH(aq)(DFT) DG(aq)(DFT)

15.1700 16.3443 15.9671 22.4397

16.1180 17.6164 16.9182 23.1895

20.1134 22.1521 21.2502 28.5667

22.9974 24.8973 24.0328 30.8920

33.8131 35.7786 34.8704 43.2264

Zn2+

Cd2+

Ru2+

DE(aq)(DFT) DE(aq)(DFT)(zpe) DH(aq)(DFT) DG(aq)(DFT)

20.6459 22.4609 21.5270 28.9101

19.5922 21.1723 20.6017 26.0824

34.2834 36.2586 35.4389 42.2212

DE(aq)(DFT) DE(aq)(DFT)(zpe) DH(aq)(DFT) DG(aq)(DFT)

Table 6 Values of DE(aq)(DFT), DE(aq)(DFT)(zpe) (zero point energy corrected), DH(aq)(DFT), and DG(aq)(DFT) at 298 K (kcal mol1: Note: 1 kcal = 4.184 kJ) for the reaction involving replacement of a trien (2,2,2-tet) by a 2,3,2-tet (see Fig. 1) ligand on the [ML(H2O)2]2+ (L = polyamine) complex in aqueous solution as simulated for divalent metal ions by the COSMO program, calculated in this work from DFT as described in the text. Also shown are the experimental values of DG(aq)(exptl) for replacement of trien by 2,3,2-tet in aqueous solution, which are obtained from the log K1 values [33] from DG(aq)(exptl) = RT ln K1.

DE(aq)(DFT) DE(zpe corr)(aq)(DFT) DH(aq)(DFT) DG(aq)(DFT) DG(aq)(exptl)

Cd2+

Zn2+

Ni2+

2.3558 2.3207 2.3956 2.4161 0.5

2.2806 2.3319 2.3320 2.5409 1.0

0.5358 1.1377 0.9330 1.8982 2.9

The conformation of the free ligands was taken to be the linear conformation, which is generally the lowest energy conformation, although selection of the conformation does not have a significant effect. The metal ions with unfilled d sub-shells were all taken to be high-spin, except for Ru(II), which was low-spin. The starting structures of the complexes for the DFT calculations were taken to be those most commonly found for a particular complex in the Cambridge Structural Database (CSD) [42]: for the tris-en complexes of Ni(II), 14 of the reported 19 structures had the lel,lel,lel conformation, so this was used for calculations on [Ni(en)3]2+; for

the tris-tn complex of Ni(II) a structure with D3 symmetry has been reported [43], which was used for [Ni(tn)3]2+, rather than an alternate one of much lower symmetry [44], which MM calculations suggested was of slightly higher energy; for the bis-dien complexes of Ni(II), of the 41 structures reported, 28 had the dien ligands coordinated to Ni(II) in a facial (fac) manner, while the remainder were meridional (mer). MM suggested the fac was slightly more stable, so that this structure was used; for the bis-dptn structure, the only reported structure is that of Rh(III) [45], which is a mer structure, which was used for the calculations on Ni(II); for the complex [Ni(dien)(H2O)3]2+ a single structure was found [46] which was fac, which was used for the calculations; for the [Ni(dptn)(H2O)3]2+ type of complex no structures were found with any metal ion, and the dptn ligand was given the same mer conformation as in the bis-dptn complex; four structures are reported1 for [Ni(2,3,2-tet)X2] complexes (X = unidentate ligand), which all have the conformation shown in Fig. 9 which was used for the DFT calculations; 18 structures are reported for [Ni(trien)X2] complexes, all of which have the folded structure shown in Fig. 9 used in the DFT calculations. A problem that arises in calculating the free energies in aqueous solution as simulated by COSMO is how to draw up the partition functions. The gas-phase expressions for the partition functions were used in the COSMO free energy calculations. It was not

1

DMOL3

is available from Accelrys, San Diego, CA.

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5

expected that this would necessarily affect the trends in DG(aq) calculated, but that it might affect the absolute calculated values of DG(aq). 3. Results and discussion The values of DE, DE(zpe) (zero point energy corrected), DH, and DG at 298 K for the reaction involving replacement of two H2O ligands by an en or a tn ligand are shown in Tables 2 and 3 for the gas-phase reactions, and in Tables 4 and 5 for the aqueous phase as simulated by COSMO. The results in Figs. 2 and 3 show that use of correlations between DG(DFT) for the reactions involving displacement of water molecules by NH3 DG(g)(DFT) or en DG(aq)(DFT) from the aqua-ions (Eqs. (1) and (2)) correlate well with log K1 for formation of the corresponding complexes of the same metal ions in aqueous solution. One can use these correlations to estimate that for Ru(II) log K1(NH3) is 4.0, and that log K1(en) is 10.1. As was found previously [30–32] for all such correlations involving NH3, the slopes of the correlations are well above unity: the slope should be 0.73 in comparing DG(DFT) with log K1 if the DFT calculations corresponded exactly with the thermodynamics in aqueous solution, whereas the slope in Fig. 3 is 2.66. This large slope was interpreted in terms of the effects of solvation, which dampens the size of DG(aq) in aqueous solution as compared to the gas-phase. In Fig. 3 the COSMO module of DMOL3 was used to simulate aqueous solution. As was found previously [49], the approach used in COSMO, where water is treated as a structureless dielectric medium, appears inadequate to bring the slope of correlations such as those in Figs. 2 and 3 down near unity. COSMO also does not appear to significantly improve the goodness of fit of such correlations. One problem would appear to be the omission of specific solvation by water molecules in programs such as COSMO, where metal ions form, for example, extensive more strongly hydrogen-bonded layers of water molecules in the outer-sphere [50], not included in Eqs. (1) and (2). A second problem may be the assumption used here that the partition functions from the gas-phase can be used to calculate DG(aq) in the COSMO simulations. The observation of correlations such as those in Figs. 2 and 3 with slopes well above unity suggests a systematic increase in energy of outer-sphere solvation of the metal ions in aqueous solution with increasing log K1 for the amine, not accounted for in the DFT calculations. It seems probable that the increasing energies of solvation due to outer-sphere waters greatly decrease experimental values of DG(aq) or DH(aq) as compared to values calculated in the gas-phase considering only inner-sphere coordinated waters. Of major interest here is the effect of chelate ring size on metal ion size-based selectivity (Scheme 1), which is the basis of a useful

bite distance = 2.83 Å

H2N best-fit M-N = 2.5 A

bite distance = 2.44 Å

NH2

H2N

NH2 M

M

o

69

(a) 5-membered chelate ring of en (ethylenediamine)

best-fit M-N = 1.5 A

~109o

(b) 6-membered chelate ring of tn (1,3-diaminopropane)

Scheme 1. Best-fit M–N bond lengths and N–M–N angles, as well as N  N ‘bite’ distances across the chelate ring, for coordinating as part of (a) a 5-membered en chelate ring and (b) a 6-membered tn chelate ring. Note: 1 Å = 100 pm.

Fig. 4. Relationship between change in log K1 on passing from dien, which forms all 5-membered chelate rings, to 2,3-tri, which forms one 5-membered and one 6membered chelate ring, and metal ion radius [47]. Log K1 values from Ref. [33]. Ionic radii for octahedral coordination geometry, except for Cu(II) which is 4-coordinate square planar. The equation for the least-squares best-fit line fitted to the experimental points is shown on the diagram, as well as R2, the coefficient of determination. The error bars indicate an estimated uncertainty in log K1 for the complexes of these ligands of 0.1 log units.

rule for design of selective ligands [1]. The chelate ring size rule states that replacement of a 5-membered chelate ring by a 6-membered chelate ring in a ligand will enhance thermodynamic selectivity for smaller relative to larger metal ions [1]. A graphical analysis of the chelate ring-size rule is shown in Fig. 4, where the change in log K1 on passing from dien (two 5-membered chelate rings) to 2,3-tri (one 6-membered and one 5-membered chelate ring) depends on metal ion radius in accord with the rule. This pair of ligands is chosen here for the analysis because the change in log K1 on change of chelate ring size is quite small. Error bars have been included on Fig. 4 based on a rough estimate that the difference in log K1 has an uncertainty of 0.1 log units. This is reasonable, because, for example, Martell and Smith report an uncertainty of 0.1 log units for the value of log K1 for Cu(II) with dien, based on the work of 18 different sets of authors. The importance of such uncertainties here is that for pairs of ligands such as dien and 2,3-tri the effect of change of chelate ring size on log K1 is not large in comparison with the uncertainties in log K1. For pairs of ligands of higher denticity such as trien and 2,3,2-tet, the effect of chelate ring size on log K1 is large in comparison with the uncertainties in log K1. This is of particular importance for the pair of ligands en and tn discussed below. The simplest example of a pair of polyamine ligands where one forms a 5-membered chelate ring where the other forms a 6-membered chelate ring are en and tn. A problem that arises in analyzing the change in log K1 in passing from en to tn is that the changes in log K1 from the en to the corresponding tn complexes are rather small, being on average 0.90 log units [33]. This presents a problem in using DFT to predict the effect of chelate ring size on complex stability in such a pair of ligands, since even for simple gas-phase reactions, the accuracy of prediction of thermodynamic changes using even very large basis sets is on the order of 1 kcal mol1 [51]. Such uncertainties do not matter in correlations such as are seen in Figs. 2 and 3, where the energy changes are much larger than the associated uncertainties, indicated on the diagrams by error bars. However, for pairs of ligands such as en and tn, the uncertainties are of the same magnitude as the changes in log K1. One might therefore not expect the DFT/COSMO calculations to predict such a small change with sufficient accuracy. The small decrease in log K1 in passing from the en to the corresponding tn complex is supported by MM [22], which shows that curves of U versus

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M–N length are quite shallow for both en and tn complexes. A pair of multidentate ligands such as the dien/2,3-tri pair in Fig. 4 shows a stronger response in log K1 in response to change of chelate ring size in comparison to the en/tn pair. This appears to be due to the fact that in bidentate ligands such as en or tn, mismatches of metal ion size and ligand geometry can be compensated for by the metal ion twisting out of the best-fit plane of the ligand, whereas in ligands of higher denticity this is not easily accomplished because of the constraining influences of other chelate rings that are part of the multidentate ligand. Larger metal ions appear able to open up the ‘bite’ (distance between the donor atoms in the chelate ring) of tn by rotating the donor atoms so that the H-atoms on the NH2 group and adjacent CH2 group are in a more eclipsed conformation. The distortion of the tn chelate ring is illustrated in Fig. 5, where it is seen that for 6-coordinate complexes of tn found in the CSD (124 structures), as the M–N bond length increases, so the bite size increases. Also included in Fig. 5 are M–N lengths and bite sizes for tn complexes from gas-phase structures generated here by DFT calculation, which show the same trend as the experimental solid state structures. The value of R2 in the correlation in Fig. 5 is 0.6677, which is acceptable, but fairly low, suggesting that other factors apart from M–N length also contribute to the bite distance in these tn complexes. One possible contributing factor could be the varying covalence of the M–N bond, which might affect the ease with which the N–M–C angle can be distorted, and so allow for opening up of the bite distance. Sc(II) has been indicated on the diagram, as it appears to be an outlier in some of the correlations discussed below, and one sees here that it deviates somewhat from the trend seen on the diagram for the other DFT-generated structures. In Fig. 6 is shown a plot of the change in DH(g)(DFT) for reaction 3 calculated by DFT in the gas-phase (DH(g)(DFT) values from Tables 2 and 3), as a function of the ionic radii (r+) for 6-coordination of the metal ions [47], except for Cu(II) and Cr(II), for which the square-planar radii for 4-coordination were used.

½MðH2 OÞ4 ennþ þ tn ! ½MðH2 OÞ4 ðtnÞnþ þ en

ð3Þ

It is seen that although the correlation has a fairly modest R2 value of 0.6144, it does support the idea that smaller metal ions such as Cu(II) favor the 6-membered chelate ring of tn more strongly than does a much larger ion such as Ca(II). The correlation includes all the M(II) ions between Ca(II) and Zn(II) in the first row of d-

Fig. 5. Relationship between N  N bite distance (distance between the N donors in the chelate ring – Scheme 1) in octahedral tn complexes, and the M–N length in the same complexes. Solid state structures (117 structures) from Ref. [42] (), or structures calculated here by DFT (h). The equation for the least-squares best-fit line fitted to the experimental points is shown on the diagram, as well as R2, the coefficient of determination.

Fig. 6. Effect of increased chelate ring size on DH of complex-formation in the gasphase, as a function of metal ion size. The plot shows DH of replacement of en (5membered chelate ring) from each metal ion by tn (6-membered chelate ring), as calculated by DFT1 in the gas-phase. These DH values are plotted against the ionic radii of the metal ions [47], which are for octahedral coordination, except for Cu(II) and Cr(II) which are the 4-coordinate square planar values. The error bars denote the typical standard deviation of 0.5 kcal mol1 found for correlation of energies of complex formation predicted by DFT with experimental values in aqueous solution. The equation for the least-squares best-fit line fitted to the experimental points is shown on the diagram, as well as R2, the coefficient of determination. The error bars on the points indicate the accuracy of about 1 kcal mol1 with which wavemechanical calculations normally predict the energies of simple gas-phase reactions [51]. Note: 1 kcal = 4.184 kJ.

block ions, as well as Cd(II). This includes the non-existent Sc(II) ion, for which an ionic radius was estimated by interpolating between the ionic radii [47] of 6-coordinate Ca(II) and Ti(II). A scan of the CSD turns up a large number of structures of Cr(II) complexes, excluding those involved in metal–metal bonding, and organometallic compounds, which suggest a rough value of r+ for square-planar Cr(II) of 0.65 Å, which was the value used here to take into account the tetragonal distortion of the Cr(II) complexes. The structure of the complex [Cr(tn)(H2O)4]2+ generated by DFT calculation here shows significant Jahn–Teller distortion, as would be expected for a high-spin d4 ion. Thus, the Cr–N bond lengths, which are in-plane, are 2.140 Å, while the in-plane Cr–O bond lengths are 2.154 Å. The axial Cr–O distances average 2.605 Å. The values in Tables 4 and 5 refer to aqueous solution simulated using the program COSMO.1 In order to analyze the thermodynamics relating to Eq. (3) in terms of metal ion size, the values for DG(g)(DFT) and DG(aq)(DFT) at 298 K calculated for Eq. (3) were plotted against the ionic radii [47] of the metal ions in Fig. 7. The DG(g)(DFT) values as well as DG(aq)(DFT) in aqueous solution simulated by COSMO are plotted in Fig. 7. The points for Sc(II) and Ti(II) are omitted from Fig. 7: these lie well off the correlations observed, and act simply to clutter up the diagram. Ti(II), and particularly Sc(II), are very unstable oxidation states. It is quite possible that the tn complexes of Ti(II) and Sc(II) show very low stability because of inhibition of the distribution of positive charge from the strongly reducing metal ion onto the tn ligand. It has already been shown in Table 1 how well a simple approach such as MM calculation can account for the differences in DH for formation of Ni(II) complexes of analogous polyamine ligands in aqueous solution, where ligands that form only 5-membered chelate rings are replaced by ligands that form at least one 6-membered chelate ring.

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Fig. 7. Plots of DG calculated by DFT for the displacement of en by tn in the gasphase (N) for [M(L)(H2O)4]2+ complexes (L = en or tn), or in aqueous solution (h) as simulated by COSMO calculations, as a function of the ionic radii of the metal ions [47]. Also shown are the experimental values of DG () in aqueous solution for the same reaction calculated from log K1 values in Ref. [33]. The equations for the leastsquares best-fit line fitted to the experimental points is shown on the diagram, as well as R2, the coefficients of determination. The points for Sc(II) and Ti(II) have been omitted as discussed in the text. The error bars on the points indicate the accuracy of about 1 kcal mol1 with which wave-mechanical calculations normally predict the energies of simple gas-phase reactions [51].

The interesting question is how well DFT can do by comparison. Fig. 7 shows that in the gas-phase there is a relatively strong response for DG(g)(DFT) for Eq. (3) to metal ion size, with a value of R2 of 0.7632. The slope of the relationship between DG(g)(DFT) and metal ion size is in agreement with the expectations from the rule that increase of chelate ring size from 5-membered to 6membered will favor the thermodynamic complex stability of smaller metal ions. The DG(g)(DFT) of replacement of en by tn is calculated to be favorable in the gas-phase for all metal ions except for the large Ca(II) ion. This greater stability of the tn compared to the en complexes in the gas phase undoubtedly reflects the larger size of tn than en, which leads to stabilization in the gas-phase by polarizability effects [52]. Polarizability effects relate to the tendency of the charge on an ion in the gas-phase to be distributed over the whole complex ion. Polarizability effects stabilize ions in the gas-phase by this distribution of ionic charge, and are largely a function of size of the complex ion. Polarizability effects are responsible for numerous reversals of basicity orders on passing from the gas-phase to aqueous solution. In the gas-phase the order of proton basicity (as measured by DG(g) for the protonation equilibrium) of methyl-substituted amines is NH3 « CH3NH2 « (CH3)2NH « (CH3)3N [52], which reflects increasing size of the amine along this series, and hence increased stabilization due to polarizability effects. In aqueous solution hydrogen bonding to the solvent quenches polarizability effects by taking over the role of distributing the ionic charge, and the order of proton basicity (as measured by the protonation constants) is now NH3 < CH3NH2  (CH3)2NH > (CH3)3N [33]. In Fig. 7 simulation of aqueous solution using COSMO appears to be quite adequate at reproducing the quenching of polarizability effects in aqueous solution. The value of DG(aq)(DFT) for Eq. (3) is now positive, in line with experimental values of DG(aq) (from DG(aq) = RT ln K) in aqueous solution. The few experimental values available [33] for DG(aq) and DH(aq) for the formation of tn complexes in aqueous solution show that the tn complexes with their 6-membered chelate rings are all thermodynamically less stable than the analogous en complexes with 5-membered chelate rings. The experimental values of DG(aq) and DH(aq) for Eq. (3) show almost no response in aqueous solu-

tion to the effects of chelate ring size in Fig. 7. The DFT calculations using COSMO to simulate aqueous solution produce a fairly weak response in DG(aq)(DFT) for reaction (3) to metal ion radius, with a low R2 value of 0.3407. The values of DG(aq)(DFT) for Eq. (3) are positive for all metal ions, indicating that the polarizability effects that stabilize the complexes of the larger tn ligand relative to those of en in the gas phase have been largely quenched by the simulated aqueous solution. At the same time, the response of DG(aq)(DFT) for Eq. (3) to metal ion size has been somewhat weakened, in line with the weak response to metal ion radius of the experimental DG(aq) results. In Fig. 7 the reasonably good R2 of 0.7632 in the correlation of DG(g)(DFT) for Eq. (3) in the gas phase with ionic radius is in contrast with the very low R2 of 0.3407 for DG simulated in aqueous solution using COSMO. The latter reflects to some extent the shallower slope of the correlation for experimental DG(aq) with ionic radius, but the points also deviate strongly from the best fit line. As discussed above, with the DFT calculations having an associated error in predicting thermodynamics for reactions in the gas-phase of about 1.0 kcal mol1 [51], the attempted correlation in Fig. 7 is reaching the limit of accuracy with which DFT can predict thermodynamic results. A possible additional contributor may be the fact that COSMO models aqueous solution as a structureless dielectric medium, where a model including specific water solvent molecules might be more accurate. An important aspect of the MM calculations in Table 1 is that they correctly account for the single instance in the Table where change of a 5-membered chelate ring to a 6-membered chelate ring leads to an increase in thermodynamic complex stability, which occurs in Eq. (4) for the case where M = Ni(II), n = 1, L = trien and L0 = 2,3,2-tet.

½MðLÞn 2þ ðaqÞ þ nL0 ðaqÞ ! ½MðL0 Þn 2þ ðaqÞ þ nLðaqÞ

ð4Þ

As seen in Table 6, the DFT calculations correctly predict that for the case where M is the small Ni(II) cation, n = 1, L = trien and L0 = 2,3,2-tet, the 2,3,2-tet complex will be thermodynamically the more stable [33]. The DFT calculations are thus able to replicate the ability of the MM calculations to predict that for the small Ni(II) cation, the 2,3,2-tet complex will be more stable than the trien complex, as is found to be the case experimentally [33]. The DFT calculations predict that for the larger Zn(II) and Cd(II) cations the 2,3,2-tet complexes will be less stable than the trien complex. Experimentally it is found that even for the larger Zn(II) and Cd(II) ions, the 2,3,2-tet complex is more stable than the trien complex, but only by a small amount. As seen below for the COSMO calculations on other larger polyamines, this may reflect the tendency of such calculations to predict thermodynamic complex stability that is progressively too large for metal ions as they become stronger Lewis acids. In Table 7 are shown values of DE(aq)(DFT), DE(aq)(DFT)(zpe) (zero point energy corrected), DH(aq)(DFT), and DG(aq)(DFT) at 298 K for the reactions in Eq. (4) for Ni(II) complexes where various ligands that form 5-membered chelate rings are replaced by ana-

Table 7 Values of DE(aq)(DFT), DE(aq)(DFT)(zpe), DH(aq)(DFT), and DG(aq)(DFT) at 298 K (kcal mol1: Note: 1 kcal = 4.184 kJ) for the reaction involving replacement of dien by dptn, or 2 dien by 2 dptn (see Fig. 1 for ligand abbreviations) ligands, or 3 en by 3 tn ligands, on the Ni(II) polyamine complexes in aqueous solution as simulated for divalent metal ions by the COSMO program, calculated in this work from DFT as described in the text.

DE(aq)(DFT) DE(aq)(DFT)(zpe corr) DH(aq)(DFT) DG(aq)(DFT)

Ni(dien)/dptn

Ni(dien)2/2dptn

Ni(en)3/3tn

3.2272 4.2916 3.8901 5.7830

12.1174 13.6072 13.0937 15.7013

9.500 9.8815 9.8604 12.3065

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logs that form 6-membered chelate rings. In Table 8 are shown the values of DH(aq)(DFT) and DG(aq)(DFT) for Eq. (4) for all those that have been calculated here for Ni(II) by DFT using the COSMO module1 to simulate aqueous solution, compared with the experimental values for DH(aq) and DG(aq) in aqueous solution [33] for Eq. (4). Table 8 shows that the DFT calculations produce values for Eq. (4) that show a similar pattern to the experimental values, but the calculated values become progressively too large by increasing amounts as the experimental values increase. Thus, for the reaction where en is replaced by tn, the calculated and experimental values of DH(aq), and DG(aq) are not too far apart in value, but where the values of DH(aq) and DG(aq) are at a maximum for the replacement of two dien ligands by two dptn ligands, the calculated values of DH(aq)(DFT) and DG(aq)(DFT) are considerably larger than the experimental values of DH(aq) and DG(aq). One finds that there is a good linear relationship between DH(aq)(DFT) calculated for Eq. (4), and the experimental values, DH(aq), as seen in Fig. 8, and also for DG(aq)(DFT) and DG(aq). The slopes of the relationships in Fig. 8 are well below one, whereas one would ex-

Table 8 Difference in DH and DG for formation of the Ni(II) complexes of some polyamine ligands as calculated by DFT using the COSMO module of DMOL3, compared with the experimental values [33]. The ligands form exclusively 5-membered chelate rings (en, dien, trien) or also one or more 6-membered chelate rings (tn, dptn, 2,3,2-tet). Coordinated waters and charges on complexes in the equilibria are omitted for simplicity. Units are kcal mol1. Note: 1 kcal = 4.184 kJ. Reaction

Ni(en) + tn = Ni(tn) + en Ni(en)3 + 3tn = Ni(tn)3 + 3en Ni(dien) + dptn = Ni(dptn) + dien Ni(dien)2 + 2 dptn = Ni(dptn) + 2 dien Ni(trien) + 2,3,2-tet = Ni(2,3,2tet) + trien

DFT

Experimental

DH(aq)

DG(aq)

DH(aq)

DG(aq)

1.70 9.86 3.9 13.1 0.93

2.63 12.3 5.78 15.7 1.90

1.4 6.4 1.3 7.7 3.9

1.4 6.3 1.9 8.0 2.9

Fig. 9. Conformations used for DFT calculations on some of the Ni(II) polyamine complexes discussed in this paper: (a) fac [Ni(dien)2]2+; (b) mer [Ni(dptn)2]2+ (c) [Ni(trien)(H2O)2]2+ (d) [Ni(2,3,2-tet)(H2O)2]2+. Drawings made with ORTEP [48].

pect slopes of unity if the DFT calculations reproduced quantitatively the experimental values of DH(aq) and DG(aq). It would appear that the COSMO approach for simulating thermodynamics in aqueous solution produces DH(aq)(DFT) and DG(aq)(DFT) values that are too large because of its failure to take into account specific solvation effects. In the case of Table 6 and Fig. 6, this failure would appear to involve differences in solvation of the ligands and not the metal ion, since the metal ion is Ni(II) in all cases. It appears that, as with the cases involving constant polyamine ligands and varying metal ions, as in Figs. 2 and 3, or a constant metal ion and varying ligands, as in Fig. 8, the DFT calculations produce good correlations DH(aq)(DFT) and DG(aq)(DFT) with experimental values of DH(aq) or DG(aq), but the slopes of the correlations are too large, which suggests that the DFT calculations are omitting the effects of specific solvation by actual water molecules, which are not accounted for in the COSMO approach where water is treated as a structureless dielectric medium. It is encouraging to note that in a recent DFT study [53] it was predicted that L1 in Fig. 1 should be highly selective for the very small Be(II) ion, which is to be expected from the presence of three 6-membered chelate rings. As will be shown in a future paper [54], chelate rings based entirely on aromatic groups, such as 8QP in Fig. 1, are much more rigid than chelate rings based on saturated groups, and show very sharp metal ion size-based selectivity.

4. Conclusions

Fig. 8. Relationship between experimental DH and DG [33] for the displacement of polyamine ligands that form exclusively 5-membered chelate rings (L) from the Ni(II) complexes by analogs that form at least one 6-membered chelate ring (L0 ), and DH and DG for the corresponding reactions calculated here by DFT. In the DFT calculations aqueous solution was simulated using the COSMO module of DMOL3.1 Units are kcal mol1. The reactions NiLn + nL0 = NiL0 n + nL are for points number: (1) n = 1, L = trien, L0 = 2,3,2-tet; (2) n = 1, L = en, L0 = tn; (3) n = 1, L = dien, L0 = dptn; (4) n = 3, L = en, L0 = tn; (5) n = 2, L = dien, L0 = dptn. A key to the ligand abbreviations is to be found in Fig. 1. The equations for the least-squares best-fit lines fitted to the experimental points are shown on the diagram, as well as R2, the coefficient of determination. The error bars on the points indicate the accuracy of about 1 kcal mol1 with which wave-mechanical calculations normally predict the energies of simple gas-phase reactions [51]. Note: 1 kcal = 4.184 kJ.

(1) The DFT calculations reported here yield values of DH(aq)(DFT) and DG(aq)(DFT) for the formation of complexes of a diamine ligand such as en with varying divalent metal ions, ranging from very weak complexes formed by Ca(II), to very strong complexes formed by Cu(II), that correlate well with the experimental DH(aq) and DG(aq) values of complex-formation in aqueous solution. Such correlations can be used to predict log K1 for metal ions such as Ru(II), for which experimental values of log K1 are currently not available. (2) Experimental values of DH(aq) and DG(aq) for the replacement of en from the [M(H2O)4en]2+ complex by tn vary little with varying metal ion size. This is rationalized in terms of the greater flexibility of a single diamine chelate ring such as is present in en or tn, as compared with a

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polyamine ligand. For polydentate ligands, the constraining effects of multiple chelate rings are such that the chelate ring is much less able to distort so as to accommodate metal ions that are not close to being a best-fit size. (3) The DFT calculations show that the DH(g)(DFT) and the DG(g)(DFT) values in the gas-phase for the replacement of an en by a tn for a variety of metal ions correlates tolerably well with metal ion radius, such that smaller metal ions favor the six-membered chelate ring formed by tn relative to larger metal ions, which favor the 5-membered chelate ring formed by en. This is in agreement with ideas on chelate ring size and metal ion selectivity [1], which state that change of chelate ring size from 5-membered to 6-membered will enhance selectivity for smaller relative to larger metal ions. (4) The DFT calculations of DH(g)(DFT) and the DG(g)(DFT) in the gas-phase show favorable thermodynamics for the replacement of en by tn for all metal ions except the very large Ca(II) ion, which is interpreted in terms of polarizability effects, that stabilize the complexes of tn relative to en, because the larger tn leads to greater dispersal of the cationic charge over the larger complex of tn. (5) Use of the COSMO program to simulate thermodynamics in aqueous solution quenches polarizability effects in the competition between en and tn, and correctly makes DG(aq)(DFT) for replacement of en by tn in aqueous solution unfavorable for all metal ions, although it is somewhat more favorable for smaller metal ions as required by the chelate ring-size rule. (6) The correlation of DG for the replacement of en by tn in aqueous solution, as simulated by COSMO, correlates poorly with metal ion size, in contrast with DG(g) and DH(g) in the gas-phase. It is concluded that this arises in part because of the small response of the aqueous phase DG(aq)(DFT) for the reaction to metal ion size, which is also the case for the experimental DG(aq) values. A contributing factor to the poor correlation of DG(aq)(DFT) for the replacement of en by tn with metal ion size may be the use in the DFT calculations of a structureless dielectric medium to represent aqueous solution. (7) For the replacement of the tetradentate polyamine trien in the [Ni(trien)(H2O)2]2+ complex by 2,3,2-tet, the DFT calculations correctly predict that this will be thermodynamically favorable, which is actually the only example considered here where that is the case for replacement of a 5-membered chelate ring by a 6-membered ring. Trien forms only 5-membered chelate rings, while 2,3,2-tet, forms one 6-membered and two 5-membered chelate rings. The chelate ring-size rule states that this should be more favorable for smaller metal ions [1]. For the larger Zn(II) and Cd(II) ions, this reaction is correctly predicted to be thermodynamically less favorable than for the smaller Ni(II) ion. (8) The correlation between calculated and experimental DH and DG values is good for replacing larger polyamine ligands that form only 5-membered chelate rings by analogous ligands that also form one or more 6-membered chelate rings, with a constant metal ion such as Ni(II). All such correlations have good R2 (coefficient of determination) values, but have slopes very different from unity, which show progressively too large DH and DG values as predicted by the DFT calculations with increasingly larger experimental values of DH and DG in aqueous solution. These slopes that differ greatly from unity in these correlations are interpreted in terms of specific solvation effects, that are not included in the COSMO approach to modeling aqueous solution. At present more sophisticated approaches to modeling thermodynamics of complex formation in aqueous solution using DFT calculations, where specific solvation is included, are being investigated. The ultimate aim is to develop this approach of using DFT calculations, where correlations are obtained between the thermodynamics calculated in the gas-phase or in simulated aqueous solution and the thermodynamics of complex formation in aqueous solution, as a tool in designing improved ligands for selective metal ion complexation.

9

Acknowledgments The authors thank the University of North Carolina Wilmington and the Department of Energy (Grant # DE-FG07-07ID14896) for generous support for this work. Appendix A. Supplementary material Pdb files containing the coordinates of the structures of the complexes generated here by DFT calculation are available as supplementary material. References [1] [2] [3] [4] [5]

[6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]

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